PHYSICAL PROPERTIES AND STRUCTURE OF FERROELECTRIC - FERROELASTIC DMAAS CRYSTALS

Size: px
Start display at page:

Download "PHYSICAL PROPERTIES AND STRUCTURE OF FERROELECTRIC - FERROELASTIC DMAAS CRYSTALS"

Transcription

1 PHYSICAL PROPERTIES AND STRUCTURE OF FERROELECTRIC - FERROELASTIC DMAAS CRYSTALS L. KIRPICHNIKO VA, A. URUSOVSKAYA, V. DOLBININA, L. SHUVALOV Institute of Crystallography, USSR Academy of Sciences, Moscow G. KIOSSE Institute of Applied Physics, Moldova Academy of Sciences, Kishinev T. DZIGRASHVILI Tbilisi Politechnical Institute, Tbilisi I NTRODUCTION Recently it has been found [1 ] that DMAAS crystals [(CH1),NH,Al(S04)2 6H,0] possess ferroelectric and ferroelastic properties. Single crystals of good quality have been grown by the evaporation method. At room temperature DMAAS crystals arc monoclinic; a = A, b = A, c = A, y = 68.13", Sp. gr. PI 12,/a or a = A, bn = A, = A, yn = 100.4", Sp. gr P1"12i/n [2]. Nearly tricritical second order phase transition takes place at Tc = 150 K with the symmetry change 2/m - m [1]. The transition can be classified as the proper ferroclectric order-disorder type. It has been found [3] that ferroelectric phase transition observed in DMAAS crystals is due to changes in the orientation mobility of sulphate and dimethylamine sublattices. No soft modes were observed in Raman spectra of both phases down to 7 cmh. Above Tc DMAAS crystals exhibit ferroelastic properties. The geometry of the domain structure and the orientation of the optical indicatrices of domain correspond to the orthorhombic symmetry of the prototype phase (mmm), but the ferroelastic phase transition does not occur up [Bull.Soc.Cat.Cien.],Vol.XI II, Num.1,1992

2 324 KIRPICfI,AI OL' I, URU.SOl'SK IYA, DOLBIN'lN'A, SFIUL'ALOV, tilo.s'sf, DZIGRASII IL1 to the decomposition temperature (358 K). The mechanical hysteresis (stress-strain) loop at room temperature is of a rectangular shape, spontaneous strain is considerable, about 10', the coercive stress is Pa. It was found [4] that mecanical properties are substantially anisotropie - the crystals showed almost no plastic deformation along the two-fold axis and were rather brittle, whereas in the plane m they showed anomalous plasticity with the yield limit 2.10' Pa, the maximum plastic deformation being 5-7%. There are two mechanisms of plastic deformation, the first one is ferroelastic twinning and the second one is gliding. Twinning is reversible, is accompanied by very weak deformation hardening, irreversible deformation due to gliding is characterized by powerful strengthening and jumpwise deformation. Here in order to understand the behaviour of DMAAS crystals upon deformation we have analyzed changes of the crystal stucture. We have considered crystallographic aspects of twinning and gliding processes and shown new data on dielectric properties of DMAAS crystals. EXPERIMENTAL 1. Electric properties Figure 1 shows results of dielectric measurements of DMAAS crystals in polar direction [110] at various biasing electric field strength and temperature dependence of tg d. The dielectric constant was measured using the E7-8 bridge at I khz, the temperature was stabilized with an accuracy of 5.10' K. As one can see from the figure, the temperature of maximum tg d is below Tc and equals 110 K. Above Tc the behaviour of c obeys the Curie-Weiss law both for E = 0 and F 0, the Curie constant C = (2.2-3) - 10' K. The data of spontaneous polarization and coercive field obtained using D - E hysteresis loop at 50 Hz are presented in figure 2. According to our measurements, the behaviour of spontaneous polarization and dielectric constant at dc electric field is typical of second-order ferroelectric phase transition. The maximum of tg b coincides in temperature with an abrupt increase of coercive field due to less mobility of ferroelectric domains. 2. Polarization microscope observation Figure 3 shows changes that occur in the sample upon compression as the load increases. One can see the changes in the specimen shape during )Rtit II.Soc.Cat. Cien.),VoLXIII,Nuln.1,1992

3 FF.RROELE (:TRI(:-FERROELAS77CUa1AA.SCR}'ST.lL.S 325 / T K 200 Fig. 1. Temperature dependence of dielectric constant t; at various biasing electric field strength: 1-0, 2-5, 3-15, 4-27 kvcm-' and 5 - tg S of DMAAS crystals. jos. 15- C/cm 2 Ec K V/cm T, K 1S0 Fig. 2. Temperature dependence of spontaneous polarization and coercive field of DMAAS crystals (50 Hz). [Butll.Soc.Cat.Cien.],Vol.XIII,Num.1,1992

4 326 KIRPIC11.AIKM 1, t RLSOI.S'K. Y1, DOLBL\7.A.1,.SHL I.ILO\, MOSSI D//GR.ISH17L1 reconstruction of ferroelastic domains under the action of compressive stress. When we stop the compression force the domain picture remains the same and specimen shape is not changed. The observations were made in polarizing microscope on the specimen perpendicular to the two-fold axis. Feroelastic domain being the reflection twins with the (110) twinning plane, appear and disappear easily under shear strain, that in practice substitutes the compression press strain. The spontaneous deformation tensor U,1 should contain two components -U12 and U,1 upon hypothetic phase transition mmm - 2/m. The twinning occurs under the action of shear deformation which can be realized_by means of compression or tension along 1130] (Sp. gr. P1121/a) or [210] (Sp. gr. P1121/n). Figure 4 shows changes that occur in the sample upon compression as the load increases fig. 3. Che change of the ferroelectric domain structure and specimen shape under external mechanical stress ( MPa ) at 300 K. hg. 4. Photograph in polarized light of a DMAAS crystal deformed by compression along 1130] with an increase in load; a, b - deformation by twinning ( MPa), c, d - deformation by gliding (2-6 MPa). [Budl.Soc.Ca t.cicn.],vo!.xll1,num.1,1992

5 FERROLLLiCTRLC- FLRROELA.STFC DMAA.S CRYSTALS 327 from 0.2 to 6 MPa at 300 K. One can readily see that first twins appear (figure 4a, b). If we increase the compression force from 2 to 6 MPa slip bands appear (figure 4c, d). The slip plane is (111), slip direction is [110]. In order to determine twinning elements such as shear plane S, twin shear direction pl and crystallographic shear s computations were made according to the program for the determination of twinning elements from structural data. Taking into account lattice constants and the twinning plane orientation found from the experiment it was found by means of special transformation that the shear plane indices S = (001). Twin shear direction was found as a transection line of shear and twinning plane: 111 = [110], crystallographic shear was estimated to be s = To illustrate the result of the computation figure 5 presents the arrangement of glide and twin elements in a DMAAS unit cell. The modulus of the Burgers vector [110] was estimated from lattice constants, B = A. Fig. 5. Arrangement of slip elements (slip plane Sp and Burgers vector B) and twinning elements (twinning plane d, shear plane S and twinning shear direction rl, in a DMAAS unit cell). 3. Structure investigations The DMAAS structure is of the ionic type [5], its basis being a framework of hydrogen bonds. The 5042 complex anions form almost regular [Butll.Soc.Cat.Cien.J.VoI.XIII, NUm.I,I992

6 3's RIRPI(JI\7RY)\ 1, I RI u)i ^h 1 ) 1, I M IJiI\I\I, MI 1 II \, RIUSW 1)/I(,RUII\7l l tetrahedra, six H,O molecules surround the A13+ ion thus building up [Al-6H,O]3+ octahedral anionic complexes that are linked with the S02- anionic complex by strong hydrogen bonds R(O-H... 0) = A. The [(CH3)2NH2]+ cations are located at void channels of this three-dimensional framework. Figure 6 shows a projection of the shear plane (001) of the DMAAS twin. Solid lines denote the structure before twinning, dotted lines after twinning. Under deformation structural elements are displaced along the (110) twinning plane. A trace of this plane is indicated by a D - D line in figure 6. Besides all almost regular SO4'- tetrahedra, [A1.6H,O]31- octahedra and [(CH3)2NH,]+ linked to them are rotated about 1001]. The hydrogen bonding system in this case is hardly distorted, the structure permits the existence of two stable positions. In case of gliding deforma tion the displacement of crystal layers relative to one another along the (111) slip plane (its trace is denoted by the S - S line in figure 6) requires larger stresses, because such displacement is accompanied by hydrogen bond rupture and defect formation. This is Fig. 6. Projection of DMAAS crystal structure on shear plane (001), D - D - trace of twinning plane (110), S - S - trace of the slip plane (111). Solid lines denote stuctural elements of the original lattice, dashed line - twinning lattice. [ButII.i.(:.it.Cien.],VoI.X[II,N6rn.1,1992

7 I, RROI:Lrc7RIC- FFRROFLASTICDtLl l.ccrystals 329 seen in figure 7 presenting a projection of the structure onto the (010) plane, where traces of slip S - S and twinning D - D are shown. A specific feature of the DMAAS structure in the paraelectric phase is complete disorder with respect to the centre of inversion of [(CH3)2NH2]+ group. The ferroelectric phase transition is, apparently, due to order these groups, their drawing near S042- tetrahedra, which results in the formation of noncompensated dipoles and appearance of Ps. Fig. 7. Projection of DMAAS structure on (010) plane. The traces of the twinning plane - D - D and slip plane S - S are shown. CONCLUSIONS 1. Upon ferroelectric twinning of DMAAS crystals the twinning plane is (110), shear plane S = (001), shear direction pl = [110], crystallographic shear s = Upon twinning under uniaxial compression perpendicular to the two-fold symmetry axis there occur rotations of almost regular SO42- tetrahedra and other structural elements about [001] as well as their displacement along the twinning plane without rupture of the hydrogen bonds. [Butll.Soc.Cat.Cifn.],Vol.XIII,N6m.1,1992

8 330 KIRPICII.A'LKOVA, URUSOVSKA l'a, DOLBININA, SIIUVALOV, KIOSSE, DZIGRASIIVIL I 3. Gliding along the (111)/[110] system is associated with rupture of hydrogen bonds and defect formation which results in a higher flow stress upon gliding as compared to the twinning flow. 4. Ferroclectricity appears due to polar common ordering of [(CH3)NH2]+ cations leading to the rotations of SO42- tetrahedra and dipole formation. ABSTRACT Ferroelectric and ferroelastic properties of new DMAAS crystals are considered. Structural changes upon gliding and twinning as well as the causes of easy processes of twinning and difficulties of gliding are found. [ButII.Soc.Cat. Cicn. ),Vol.XI I I,Num.1,1992

9 11 RROI LLC JRIC-LLRRC)11ISI7CU.il:l.aSCIZI'S/.ILS 331 REFERENCES 1. L. F. KIRPICHNIKOVA, L. A. SHUVALOV, N. R. IVANov. B. N. PRASOLov, and E. F. ANDRLYEV, Ferroelectrics, 1989, v. 96, p G. A. Klossc, I. M. RAZDOBRLL.v, and L. F. KIRPIcHNIKOVA, Izv. AN SSSR, Ser, Fiz, 1990, v. 54, p V. I. TORGASHLV, YU. 1. YUZYUK, L. F. KIRPICHNIKOVA, and L. A. SHUVALOV, Ferroelectrics, 1990, v. 110, p L. F. KIRPICIINIKOVA, A. A. URUSOVSKAYA, L. A. SHUVALOV,and V. I. MOZGOvoY, Ferroelectrics, 1990, v. 111, p I. M RAZDOBRI l v, and G. A. Kiossr:, Abstracts of the XXI All-Union Conference on Ierroclectric Physics, Rostov-on-Don, v. 2, 1989, p. 10. [Budl.Soc.Cat.Cien.j,VoLXlll,Num.1,1992

Introduction to solid state physics

Introduction to solid state physics PHYS 342/555 Introduction to solid state physics Instructor: Dr. Pengcheng Dai Professor of Physics The University of Tennessee (Room 407A, Nielsen, 974-1509) Chapter 13: Dielectrics and ferroelectrics

More information

Dielectric Study of the Ferroelectric Phase Transition in DMAGaS Crystal

Dielectric Study of the Ferroelectric Phase Transition in DMAGaS Crystal Dielectric Study of the Ferroelectric Phase Transition in DMAGaS Crystal R. Tchukvinskyi, R. Cach, and Z. Czapla Institute of Experimental Physics, University of Wroclaw, M. Borna 9, 50-204 Wroclaw, Poland

More information

PHASE TRANSITIONS IN (CH3NH3)5B12X11 (X = Cl, Br) CRYSTALS H. PYKACZ, J. MRÓZ

PHASE TRANSITIONS IN (CH3NH3)5B12X11 (X = Cl, Br) CRYSTALS H. PYKACZ, J. MRÓZ Vol. 84 (1993) ACTA PHYSICA POLONICA A Νo. 6 PHASE TRANSITIONS IN (CH3NH3)5B12X11 (X = Cl, Br) CRYSTALS H. PYKACZ, J. MRÓZ Institute of Physics, Technical University of Wroclaw Wybrzeże Wyspiańskiego 27,

More information

Supplementary Figure 1: Crystal structure of CRCA viewed along the crystallographic b -direction.

Supplementary Figure 1: Crystal structure of CRCA viewed along the crystallographic b -direction. Supplementary Figure 1: Crystal structure of CRCA viewed along the crystallographic b-direction. Open arrows compare the direction and relative amplitudes of the (total) theoretical polarization vector

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi: 1.138/nature8731 Here we supplement the results of the X-ray crystallographic analysis at room temperature and detail procedures for evaluation of spontaneous polarization of the croconic acid crystal.

More information

OH) 3 CNH 3. Institute of Low Temperature and Structure Research Polish Academy of Sciences Okólna 2, Wrocław, Poland

OH) 3 CNH 3. Institute of Low Temperature and Structure Research Polish Academy of Sciences Okólna 2, Wrocław, Poland Structure and Properties of [(CH 2 OH) 3 CNH 3 ]H 2 AsO 4 A. Waśkowska, S. Dacko a, and Z. Czapla a Institute of Low Temperature and Structure Research Polish Academy of Sciences Okólna 2, 50-422 Wrocław,

More information

Ferroelectric Phenomena in Crystals

Ferroelectric Phenomena in Crystals В. А. Strukov А. Р. Levanyuk Ferroelectric Phenomena in Crystals Physical Foundations With 153 Figures and 14 Tables Springer Contents 1. General Characteristics of Structural Phase Transitions in Crystals

More information

The electric field induced strain behavior of single. PZT piezoelectric ceramic fiber

The electric field induced strain behavior of single. PZT piezoelectric ceramic fiber The electric field induced strain behavior of single PZT piezoelectric ceramic fiber Xiong Yang a, Jing Zhou a,*, Sen Zhang a, Jie Shen b, Jing Tian a, Wen Chen a, Qi Zhang ac a State Key Laboratory of

More information

Roger Johnson Structure and Dynamics: Displacive phase transition Lecture 9

Roger Johnson Structure and Dynamics: Displacive phase transition Lecture 9 9.1. Summary In this Lecture we will consider structural phase transitions characterised by atomic displacements, which result in a low temperature structure that is distorted compared to a higher temperature,

More information

Module-4. Mechanical Properties of Metals

Module-4. Mechanical Properties of Metals Module-4 Mechanical Properties of Metals Contents ) Elastic deformation and Plastic deformation ) Interpretation of tensile stress-strain curves 3) Yielding under multi-axial stress, Yield criteria, Macroscopic

More information

Classification of Dielectrics & Applications

Classification of Dielectrics & Applications Classification of Dielectrics & Applications DIELECTRICS Non-Centro- Symmetric Piezoelectric Centro- Symmetric Pyroelectric Non- Pyroelectric Ferroelectrics Non-Ferroelectric Piezoelectric Effect When

More information

Antiferroelectric ADP doping in ferroelectric TGS crystals

Antiferroelectric ADP doping in ferroelectric TGS crystals June 2002 Materials Letters 54 (2002) 329 336 www.elsevier.com/locate/matlet Antiferroelectric ADP doping in ferroelectric TGS crystals G. Arunmozhi*, S. Lanceros-Méndez, E. de Matos Gomes Departamento

More information

Structure and Dynamics : An Atomic View of Materials

Structure and Dynamics : An Atomic View of Materials Structure and Dynamics : An Atomic View of Materials MARTIN T. DOVE Department ofearth Sciences University of Cambridge OXFORD UNIVERSITY PRESS Contents 1 Introduction 1 1.1 Observations 1 1.1.1 Microscopic

More information

OH) 3. Institute of Experimental Physics, Wrocław University, M. Born Sq. 9, Wrocław, Poland

OH) 3. Institute of Experimental Physics, Wrocław University, M. Born Sq. 9, Wrocław, Poland Structure and Phase Transition of [(CH 2 OH) 3 CNH 3 ] 2 SiF B. Kosturek, Z. Czapla, and A. Waśkowska a Institute of Experimental Physics, Wrocław University, M. Born Sq. 9, 50-204 Wrocław, Poland a Institute

More information

INFLUENCE OF DEFECTS ON FERROELASTIC PHASE TRANSITION IN InI SINGLE CRYSTALS M.'. KOLINKO, I.V. KITΥK AND A.B. KOZHLJUK

INFLUENCE OF DEFECTS ON FERROELASTIC PHASE TRANSITION IN InI SINGLE CRYSTALS M.'. KOLINKO, I.V. KITΥK AND A.B. KOZHLJUK Vol. 84 (1993) ACTA PHYSICA POLONICA Α No. 6 INFLUENCE OF DEFECTS ON FERROELASTIC PHASE TRANSITION IN InI SINGLE CRYSTALS M.'. KOLINKO, I.V. KITΥK AND A.B. KOZHLJUK Physical Faculty, Lviv I. Franko University,

More information

Ferroelectric Materials

Ferroelectric Materials Ferroelectric Materials The permanent electric dipole moment possessed by all pyroelectric [polar] materials may, in certain cases, be reoriented by the application of an electric field. Such crystals

More information

Materials 218/UCSB: Phase transitions and polar materials

Materials 218/UCSB: Phase transitions and polar materials Materials 218/UCSB: Phase transitions and polar materials Ram Seshadri (seshadri@mrl.ucsb.edu) Background: Intrinsic stability of thermodynamic systems (after H. B. Callen, Thermodynamics and an introduction

More information

3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS

3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS 3.091 Introduction to Solid State Chemistry Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS 1. INTRODUCTION Crystals are held together by interatomic or intermolecular bonds. The bonds can be covalent,

More information

Outline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour

Outline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard

More information

Mechanics of Earthquakes and Faulting

Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Surface and body forces Tensors, Mohr circles. Theoretical strength of materials Defects Stress concentrations Griffith failure

More information

Ferroelectrics and ferroelectric domains

Ferroelectrics and ferroelectric domains Ferroelectrics and ferroelectric domains MatjažPanjan mentor: dr. Peter Prelovšek. April 003 Abstract This seminar gives introduction to ferroelectricity, ferroelectric domains and domain walls. There

More information

Synthesis and Ferroelectric Properties of KNO 3 films

Synthesis and Ferroelectric Properties of KNO 3 films Synthesis and Ferroelectric Properties of KNO 3 films Shahid Ramay and Muhammad Sabieh Anwar LUMS School of Science and Engineering Friday, August, 20, 2010 Potassium nitrate (KNO 3 ) shows ferroelectric

More information

in a LiNH 4 SO 4 Single Crystal

in a LiNH 4 SO 4 Single Crystal Ae Ran Lim et al.: 7 Li Spin±Lattice Relaxation Time in LiNH 4 SO 4 Single Crystal 375 phys. stat. sol. (b) 214, 375 (1999) Subject classification: 76.60.Es; 64.70.Kb; S11.1 7 Li Spin±Lattice Relaxation

More information

1. The Properties of Fluids

1. The Properties of Fluids 1. The Properties of Fluids [This material relates predominantly to modules ELP034, ELP035] 1.1 Fluids 1.1 Fluids 1.2 Newton s Law of Viscosity 1.3 Fluids Vs Solids 1.4 Liquids Vs Gases 1.5 Causes of viscosity

More information

Structural Analysis I Chapter 4 - Torsion TORSION

Structural Analysis I Chapter 4 - Torsion TORSION ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate

More information

Materials and Devices in Electrical Engineering

Materials and Devices in Electrical Engineering Examination WS 01/02 Materials and Devices in Electrical Engineering Monday 11 th of March, 9:00 to 11:00, SR 203, International Department building It is allowed to use any kind of media (books, scripts,

More information

Bending Load & Calibration Module

Bending Load & Calibration Module Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of

More information

Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige

Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness

More information

A Study of Temperature Dependent Superprotonic Conductivity of Na + (1 mol%) doped [K 0.50 (NH 4 ) 0.50 ] 3 H(SO 4 ) 2 Mixed Crystal

A Study of Temperature Dependent Superprotonic Conductivity of Na + (1 mol%) doped [K 0.50 (NH 4 ) 0.50 ] 3 H(SO 4 ) 2 Mixed Crystal A Study of Temperature Dependent Superprotonic Conductivity of Na + (1 mol%) doped [K 0.50 (NH 4 ) 0.50 ] 3 H(SO 4 ) 2 Mixed Crystal Khin Kyu Kyu Han 1, Win Kyaw 2 and Win Win Thar 3 Abstract Na + (1 mol%)

More information

Materials and Devices in Electrical Engineering

Materials and Devices in Electrical Engineering Examination WS 02/03 Materials and Devices in Electrical Engineering Monday 17 th of March, 9:00 11:00, International Department, SR. 203 Notice 1. It is allowed to use any kind of aids (books, scripts,

More information

Ch. 12 Section 1: Introduction to Chemical Bonding

Ch. 12 Section 1: Introduction to Chemical Bonding Name Period Date Chemical Bonding & Intermolecular Forces (Chapter 12, 13 &14) Fill-in the blanks during the PowerPoint presentation in class. Ch. 12 Section 1: Introduction to Chemical Bonding Chemical

More information

The Antiferroelectric Ferroelectric Phase Transition in Lead-Containing and Lead-Free Perovskite Ceramics

The Antiferroelectric Ferroelectric Phase Transition in Lead-Containing and Lead-Free Perovskite Ceramics Materials Science and Engineering Publications Materials Science and Engineering 2011 The Antiferroelectric Ferroelectric Phase Transition in Lead-Containing and Lead-Free Perovskite Ceramics Xiaoli Tan

More information

Inorganic Chemistry 412 Final Exam 110 minutes. (a) Disproportionation of an acidic aqueous solution of sodium chlorite, NaClO 2.

Inorganic Chemistry 412 Final Exam 110 minutes. (a) Disproportionation of an acidic aqueous solution of sodium chlorite, NaClO 2. NAME: KEY Inorganic Chemistry 412 inal Exam 110 minutes Please show all work, partial credit may be awarded. 1. or each of the following, provide a balanced reaction. [8 pts each] (a) Disproportionation

More information

Chapter 10. Lesson Starter. Why did you not smell the odor of the vapor immediately? Explain this event in terms of the motion of molecules.

Chapter 10. Lesson Starter. Why did you not smell the odor of the vapor immediately? Explain this event in terms of the motion of molecules. Preview Lesson Starter Objectives The Kinetic-Molecular Theory of Gases The Kinetic-Molecular Theory and the Nature of Gases Deviations of Real Gases from Ideal Behavior Section 1 The Kinetic-Molecular

More information

Laboratory 4 Bending Test of Materials

Laboratory 4 Bending Test of Materials Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective

More information

Exercise: concepts from chapter 8

Exercise: concepts from chapter 8 Reading: Fundamentals of Structural Geology, Ch 8 1) The following exercises explore elementary concepts associated with a linear elastic material that is isotropic and homogeneous with respect to elastic

More information

13 Solid materials Exam practice questions

13 Solid materials Exam practice questions Pages 206-209 Exam practice questions 1 a) The toughest material has the largest area beneath the curve the answer is C. b) The strongest material has the greatest breaking stress the answer is B. c) A

More information

Chapter 7. Highlights:

Chapter 7. Highlights: Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true

More information

G. Ravichandran Aeronautics & Mechanical Engineering Graduate Aeronautical Laboratories California Institute of Technology

G. Ravichandran Aeronautics & Mechanical Engineering Graduate Aeronautical Laboratories California Institute of Technology Multi-Disciplinary University Initiative Army Research Office Engineering Microstructural Complexity in Ferroelectric Devices Mechanical Characterization G. Ravichandran Aeronautics & Mechanical Engineering

More information

6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and

6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and 6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile

More information

Intermolecular Forces and Liquids and Solids Chapter 11

Intermolecular Forces and Liquids and Solids Chapter 11 Intermolecular Forces and Liquids and Solids Chapter 11 A phase is a homogeneous part of the system in contact with other parts of the system but separated from them by a well defined boundary. Phases

More information

ME 243. Mechanics of Solids

ME 243. Mechanics of Solids ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

More information

Lecture contents. Stress and strain Deformation potential. NNSE 618 Lecture #23

Lecture contents. Stress and strain Deformation potential. NNSE 618 Lecture #23 1 Lecture contents Stress and strain Deformation potential Few concepts from linear elasticity theory : Stress and Strain 6 independent components 2 Stress = force/area ( 3x3 symmetric tensor! ) ij ji

More information

Joshua Cody Frederick Iowa State University. Iowa State University Capstones, Theses and Dissertations. Graduate Theses and Dissertations

Joshua Cody Frederick Iowa State University. Iowa State University Capstones, Theses and Dissertations. Graduate Theses and Dissertations Graduate Theses and Dissertations Iowa State University Capstones, Theses and Dissertations 2010 Strains and polarization developed during electric field-induced antiferroelectric to ferroelectric phase

More information

Specific features of hypersonic damping in relaxor ferroelectrics

Specific features of hypersonic damping in relaxor ferroelectrics Specific features of hypersonic damping in relaxor ferroelectrics Authors: I.G. Siny, S.G. Lushnikov, C.-S. Tu, and V.Hugo Schmidt This is an Accepted Manuscript of an article published in Ferroelectrics

More information

Condensed Matter A Week 2: Crystal structure (II)

Condensed Matter A Week 2: Crystal structure (II) QUEEN MARY, UNIVERSITY OF LONDON SCHOOL OF PHYSICS AND ASTRONOMY Condensed Matter A Week : Crystal structure (II) References for crystal structure: Dove chapters 3; Sidebottom chapter. Last week we learnt

More information

Strain Measurement. Prof. Yu Qiao. Department of Structural Engineering, UCSD. Strain Measurement

Strain Measurement. Prof. Yu Qiao. Department of Structural Engineering, UCSD. Strain Measurement Strain Measurement Prof. Yu Qiao Department of Structural Engineering, UCSD Strain Measurement The design of load-carrying components for machines and structures requires information about the distribution

More information

Landau-Ginzburg model for antiferroelectric phase transitions based on microscopic symmetry

Landau-Ginzburg model for antiferroelectric phase transitions based on microscopic symmetry PHYSICAL REVIEW B VOLUME 62, NUMBER 2 1 JULY 2000-II Landau-Ginzburg model for antiferroelectric phase transitions based on microscopic symmetry Richard A. Hatt Materials Research Laboratory, The Pennsylvania

More information

Stress-Strain Behavior

Stress-Strain Behavior Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

More information

Plastic Anisotropy: Relaxed Constraints, Theoretical Textures

Plastic Anisotropy: Relaxed Constraints, Theoretical Textures 1 Plastic Anisotropy: Relaxed Constraints, Theoretical Textures Texture, Microstructure & Anisotropy Last revised: 11 th Oct. 2016 A.D. Rollett 2 The objective of this lecture is to complete the description

More information

INTRODUCTION TO STRAIN

INTRODUCTION TO STRAIN SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,

More information

We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors

We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists 3,900 116,000 120M Open access books available International authors and editors Downloads Our

More information

Example-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium

Example-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic

More information

Phase Transitions in Relaxor Ferroelectrics

Phase Transitions in Relaxor Ferroelectrics Phase Transitions in Relaxor Ferroelectrics Matthew Delgado December 13, 2005 Abstract This paper covers the properties of relaxor ferroelectrics and considers the transition from the paraelectric state

More information

Electro-shape-memory effect in Mn-doped BaTiO 3 single crystals and in situ observation of the reversible domain switching

Electro-shape-memory effect in Mn-doped BaTiO 3 single crystals and in situ observation of the reversible domain switching Materials Science and Engineering A 438 440 (2006) 354 359 Electro-shape-memory effect in Mn-doped BaTiO 3 single crystals and in situ observation of the reversible domain switching L.X. Zhang a,b,c,,x.ren

More information

6.37 Determine the modulus of resilience for each of the following alloys:

6.37 Determine the modulus of resilience for each of the following alloys: 6.37 Determine the modulus of resilience for each of the following alloys: Yield Strength Material MPa psi Steel alloy 550 80,000 Brass alloy 350 50,750 Aluminum alloy 50 36,50 Titanium alloy 800 116,000

More information

Ionic Bonds. H He: ... Li Be B C :N :O :F: :Ne:

Ionic Bonds. H He: ... Li Be B C :N :O :F: :Ne: Ionic Bonds Valence electrons - the electrons in the highest occupied energy level - always electrons in the s and p orbitals - maximum of 8 valence electrons - elements in the same group have the same

More information

The (magnetic) Helmholtz free energy has proper variables T and B. In differential form. and the entropy and magnetisation are thus given by

The (magnetic) Helmholtz free energy has proper variables T and B. In differential form. and the entropy and magnetisation are thus given by 4.5 Landau treatment of phase transitions 4.5.1 Landau free energy In order to develop a general theory of phase transitions it is necessary to extend the concept of the free energy. For definiteness we

More information

Adaptive ferroelectric states in systems with low domain wall energy: Tetragonal microdomains

Adaptive ferroelectric states in systems with low domain wall energy: Tetragonal microdomains Adaptive ferroelectric states in systems with low domain wall energy: Tetragonal microdomains Y. M. Jin, Y. U. Wang, A. G. Khachaturyan, J. F. Li, and D. Viehland Citation: Journal of Applied Physics 94,

More information

STRESS UPDATE ALGORITHM FOR NON-ASSOCIATED FLOW METAL PLASTICITY

STRESS UPDATE ALGORITHM FOR NON-ASSOCIATED FLOW METAL PLASTICITY STRESS UPDATE ALGORITHM FOR NON-ASSOCIATED FLOW METAL PLASTICITY Mohsen Safaei 1, a, Wim De Waele 1,b 1 Laboratorium Soete, Department of Mechanical Construction and Production, Ghent University, Technologiepark

More information

Module 5: Failure Criteria of Rock and Rock masses. Contents Hydrostatic compression Deviatoric compression

Module 5: Failure Criteria of Rock and Rock masses. Contents Hydrostatic compression Deviatoric compression FAILURE CRITERIA OF ROCK AND ROCK MASSES Contents 5.1 Failure in rocks 5.1.1 Hydrostatic compression 5.1.2 Deviatoric compression 5.1.3 Effect of confining pressure 5.2 Failure modes in rocks 5.3 Complete

More information

IOP Conference Series: Materials Science and Engineering. Related content PAPER OPEN ACCESS

IOP Conference Series: Materials Science and Engineering. Related content PAPER OPEN ACCESS IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Distributions of energy storage rate and microstructural evolution in the area of plastic strain localization during uniaxial

More information

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina Module III - Macro-mechanics of Lamina Lecture 23 Macro-Mechanics of Lamina For better understanding of the macromechanics of lamina, the knowledge of the material properties in essential. Therefore, the

More information

Electric field dependent sound velocity change in Ba 1 x Ca x TiO 3 ferroelectric perovskites

Electric field dependent sound velocity change in Ba 1 x Ca x TiO 3 ferroelectric perovskites Indian Journal of Pure & Applied Physics Vol. 49, February 2011, pp. 132-136 Electric field dependent sound velocity change in Ba 1 x Ca x TiO 3 ferroelectric perovskites Dushyant Pradeep, U C Naithani

More information

Mechanics of Earthquakes and Faulting

Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting Lectures & 3, 9/31 Aug 017 www.geosc.psu.edu/courses/geosc508 Discussion of Handin, JGR, 1969 and Chapter 1 Scholz, 00. Stress analysis and Mohr Circles Coulomb Failure

More information

Ferroelectric materials contain one or more polar axes along which a spontaneous

Ferroelectric materials contain one or more polar axes along which a spontaneous Chapter 3 Ferroelectrics 3.1 Definition and properties Ferroelectric materials contain one or more polar axes along which a spontaneous polarization can be developed below the material s Curie temperature.

More information

Ionic and Covalent Bonding

Ionic and Covalent Bonding 1. Define the following terms: a) valence electrons Ionic and Covalent Bonding the electrons in the highest occupied energy level always electrons in the s and p orbitals maximum of 8 valence electrons

More information

, to obtain a way to calculate stress from the energy function U(r).

, to obtain a way to calculate stress from the energy function U(r). BIOEN 36 014 LECTURE : MOLECULAR BASIS OF ELASTICITY Estimating Young s Modulus from Bond Energies and Structures First we consider solids, which include mostly nonbiological materials, such as metals,

More information

Twinning Engineering Programmes (TEP) & Thammasat English Programme of Engineering (TEPE) Faculty of Engineering, Thammasat University

Twinning Engineering Programmes (TEP) & Thammasat English Programme of Engineering (TEPE) Faculty of Engineering, Thammasat University " Twinning Engineering Programmes (TEP) & Thammasat English Programme of Engineering (TEPE) Faculty of Engineering, Thammasat University Undergraduate Examination 2 nd Semester of 2019 (Mid-term) CE221:

More information

Chapter 2: Elasticity

Chapter 2: Elasticity OHP 1 Mechanical Properties of Materials Chapter 2: lasticity Prof. Wenjea J. Tseng ( 曾文甲 ) Department of Materials ngineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W.F.

More information

AP* Chapter 10. Liquids and Solids. Friday, November 22, 13

AP* Chapter 10. Liquids and Solids. Friday, November 22, 13 AP* Chapter 10 Liquids and Solids AP Learning Objectives LO 1.11 The student can analyze data, based on periodicity and the properties of binary compounds, to identify patterns and generate hypotheses

More information

Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur

Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9 Table of Contents 1. Plasticity:... 3 1.1 Plastic Deformation,

More information

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES 30 SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES * Gas molecules are small compared to the space between them. * Gas molecules move in straight lines

More information

Chap. 7. Dielectric Materials and Insulation

Chap. 7. Dielectric Materials and Insulation Chap. 7. Dielectric Materials and Insulation - The parallel plate capacitor with free space as an insulator: - The electric dipole moment for a pair of opposite changes +Q and -Q separated by a finite

More information

Ferroelectrics investigation

Ferroelectrics investigation Ferroelectrics investigation. Introduction A dielectric is understood as a material where the electric field induces an electric momentum. Let s consider a vacuum capacitor made of two planar metallic

More information

What we should know about mechanics of materials

What we should know about mechanics of materials What we should know about mechanics of materials 0 John Maloney Van Vliet Group / Laboratory for Material Chemomechanics Department of Materials Science and Engineering Massachusetts Institute of Technology

More information

Chapter 10. Liquids and Solids

Chapter 10. Liquids and Solids Chapter 10 Liquids and Solids Chapter 10 Table of Contents 10.1 Intermolecular Forces 10.2 The Liquid State 10.3 An Introduction to Structures and Types of Solids 10.4 Structure and Bonding in Metals 10.5

More information

CHAPTER-4 Dielectric Study

CHAPTER-4 Dielectric Study CHAPTER-4 Dielectric Study Dielectric Study 4.1 Introduction The characterization of dielectric ceramics has received considerable scientific interest because of their enormous applications in electronic

More information

- intermolecular forces forces that exist between molecules

- intermolecular forces forces that exist between molecules Chapter 11: Intermolecular Forces, Liquids, and Solids - intermolecular forces forces that exist between molecules 11.1 A Molecular Comparison of Liquids and Solids - gases - average kinetic energy of

More information

Structural Metals Lab 1.2. Torsion Testing of Structural Metals. Standards ASTM E143: Shear Modulus at Room Temperature

Structural Metals Lab 1.2. Torsion Testing of Structural Metals. Standards ASTM E143: Shear Modulus at Room Temperature Torsion Testing of Structural Metals Standards ASTM E143: Shear Modulus at Room Temperature Purpose To determine the shear modulus of structural metals Equipment Tinius-Olsen Lo-Torq Torsion Machine (figure

More information

Chapter 6: Plastic Theory

Chapter 6: Plastic Theory OHP Mechanical Properties of Materials Chapter 6: Plastic Theory Prof. Wenjea J. Tseng 曾文甲 Department of Materials Engineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W. F.

More information

Sample geometry and the brittle-ductile behavior of edge cracks in 3D atomistic simulations by molecular dynamics

Sample geometry and the brittle-ductile behavior of edge cracks in 3D atomistic simulations by molecular dynamics Sample geometry and the brittle-ductile behavior of edge cracks in 3D atomistic simulations by molecular dynamics V. Pelikán, P. Hora, A. Machová, R. Kolman, A. Uhnáková Institute of Thermomechanics AS

More information

REVIEW : INTRODUCTION TO THE MOLECULAR ORIGINS OF MECHANICAL PROPERTIES QUANTITATIVE TREATMENT OF INTERATOMIC BONDING : THE LENNARD-JONES POTENTIAL

REVIEW : INTRODUCTION TO THE MOLECULAR ORIGINS OF MECHANICAL PROPERTIES QUANTITATIVE TREATMENT OF INTERATOMIC BONDING : THE LENNARD-JONES POTENTIAL LECTURE #19 : 3.11 MECANICS OF MATERIALS F3 INSTRUCTOR : Professor Christine Ortiz OFFICE : 13-422 PONE : 452-384 WWW : http://web.mit.edu/cortiz/www REVIEW : INTRODUCTION TO TE MOLECULAR ORIGINS OF MECANICAL

More information

Chapter 10. Liquids and Solids

Chapter 10. Liquids and Solids Chapter 10 Liquids and Solids Section 10.1 Intermolecular Forces Section 10.1 Intermolecular Forces Section 10.1 Intermolecular Forces Section 10.1 Intermolecular Forces Metallic bonds Covalent bonds Ionic

More information

C. C. WILSON. ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX 11 OQX, UK

C. C. WILSON. ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX 11 OQX, UK Structural studies of schultenite in the temperature range 125-324 K by pulsed single crystal neutron diffraction- hydrogen ordering and structural distortions C. C. WILSON ISIS Facility, Rutherford Appleton

More information

CRYSTAL STRUCTURE OF Κ3Νa(SeO4)2 AT 340 Κ T. FUKAMI*

CRYSTAL STRUCTURE OF Κ3Νa(SeO4)2 AT 340 Κ T. FUKAMI* Vol. 94 (1998) ACtA PHYSICA POLONICA A Νο. 5-6 CRYSTAL STRUCTURE OF Κ3Νa(SeO4)2 AT 340 Κ T. FUKAMI* Department of Physics and Earth Sciences, Faculty of Science University of the Ryukyus, Okinawa 903-0213,

More information

Solid State Theory Physics 545

Solid State Theory Physics 545 olid tate Theory hysics 545 Mechanical properties of materials. Basics. tress and strain. Basic definitions. Normal and hear stresses. Elastic constants. tress tensor. Young modulus. rystal symmetry and

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.

More information

Micromechanical modeling and simulation of piezoceramic materials

Micromechanical modeling and simulation of piezoceramic materials Micromechanical modeling and simulation of piezoceramic materials B. Delibas 1, A. Arockia Rajan 1 & W. Seemann 2 1 Workgroup for Machine Dynamics, Technical University of Kaiserslautern, Germany 2 Institut

More information

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

More information

In situ observation of reversible domain switching in aged Mn-doped BaTiO 3 single crystals

In situ observation of reversible domain switching in aged Mn-doped BaTiO 3 single crystals PHYSICAL REVIEW B 71, 174108 2005 In situ observation of reversible domain switching in aged Mn-doped BaTiO 3 single crystals L. X. Zhang 1,2,3 and X. Ren 1,2, * 1 Multi-Disciplinary Materials Research

More information

N = N A Pb A Pb. = ln N Q v kt. = kt ln v N

N = N A Pb A Pb. = ln N Q v kt. = kt ln v N 5. Calculate the energy for vacancy formation in silver, given that the equilibrium number of vacancies at 800 C (1073 K) is 3.6 10 3 m 3. The atomic weight and density (at 800 C) for silver are, respectively,

More information

INVESTIGATION OF TEMPERATURE DEPENDENCES OF ELECTROMECHANICAL PROPERTIES OF PLZT CERAMICS

INVESTIGATION OF TEMPERATURE DEPENDENCES OF ELECTROMECHANICAL PROPERTIES OF PLZT CERAMICS Molecular and Quantum Acoustics vol. 28 (2007) 47 INVESTIGATION OF TEMPERATURE DEPENDENCES OF ELECTROMECHANICAL PROPERTIES OF PLZT CERAMICS M. CZERWIEC, R. ZACHARIASZ and J. ILCZUK Department of Material

More information

Tensorial and physical properties of crystals

Tensorial and physical properties of crystals Tensorial and physical properties of crystals Michele Catti Dipartimento di Scienza dei Materiali, Universita di Milano Bicocca, Milano, Italy (catti@mater.unimib.it) MaThCryst Nancy 2005 International

More information

Phenomenological Theory of a Single Domain Wall in Uniaxial Trigonal Ferroelectrics: Lithium Niobate and Lithium Tantalate

Phenomenological Theory of a Single Domain Wall in Uniaxial Trigonal Ferroelectrics: Lithium Niobate and Lithium Tantalate Accepted in PRB, 005 Phenomenological Theory of a Single Domain Wall in Uniaxial Trigonal Ferroelectrics: Lithium Niobate and Lithium Tantalate David A Scrymgeour and Venkatraman Gopalan Department of

More information

Addition 1. Shear Stack Piezoelectric Elements and Shear Effect Basics

Addition 1. Shear Stack Piezoelectric Elements and Shear Effect Basics 120 Addition 1 Shear Stack Piezoelectric Elements and Shear Effect Basics Introduction The STM scanner built up in this work is a Besocke type scanner (see room temperature STM instrumental chapter). The

More information

Materials and Devices in Electrical Engineering

Materials and Devices in Electrical Engineering Solution for Examination WS 0/0 Materials and Devices in Electrical Engineering Monday 17 th of March, 9:00 11:00, International Department, SR. 0 Notice 1. It is allowed to use any kind of aids (books,

More information

Mechanical Properties of Materials

Mechanical Properties of Materials Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

More information

MATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?

MATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition

More information

STRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING

STRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING STRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING 1 YEDITEPE UNIVERSITY ENGINEERING FACULTY MECHANICAL ENGINEERING LABORATORY 1. Objective: Strain Gauges Know how the change in resistance

More information